Question $(3 x-2)^{2}$

Studdy Solution

STEP 1

1. We are given the expression $(3x - 2)^2$ .
2. The task is to expand this expression.

STEP 2

1. Recognize the expression as a binomial square.
2. Apply the binomial expansion formula.
3. Simplify the expanded expression.

STEP 3

Recognize that $(3x - 2)^2$ is a binomial square of the form $(a - b)^2$ , where $a = 3x$ and $b = 2$ .

STEP 4

Apply the binomial expansion formula $(a - b)^2 = a^2 - 2ab + b^2$ .
For $(3x - 2)^2$ , substitute $a = 3x$ and $b = 2$ :
$(3x - 2)^2 = (3x)^2 - 2(3x)(2) + (2)^2$

STEP 5

Calculate each term in the expansion:
1. $(3x)^2 = 9x^2$
2. $-2(3x)(2) = -12x$
3. $(2)^2 = 4$

STEP 6

Combine the calculated terms to form the expanded expression:
$(3x - 2)^2 = 9x^2 - 12x + 4$
The expanded expression is:
$\boxed{9x^2 - 12x + 4}$

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